本文是计算机专业的留学生作业范例，题目是“Multiple Churn Prediction Techniques And Algorithms Computer Science Essay（多种流失预测技术和算法计算机科学论文）”，客户流失是一个商业术语，用来描述客户或客户的流失。银行、电信公司、isp、保险公司等使用客户流失分析和客户流失率作为他们的关键业务指标之一，因为留住现有客户远比获取新客户要少。企业都有专门的部门，试图赢回流失的客户，因为恢复的长期客户对公司来说比新客户更有价值。

Abstract 摘要

Customer churn is the business term that is used to describe loss of clients or customers. Banks, Telecom companies, ISPs, Insurance firms, etc. use customer churn analysis and customer churn rate as one of their key business metrics, because retaining an existing customer is far less than acquiring a new one. Corporates have dedicated departments which attempt to win back defecting clients, because recovered long term customers can be worth much more to a company than newly recruited clients.

Customer Churn can be categorized into voluntary churn and involuntary churn. In voluntary churn, customer decides to switch to another service provider, whereas in involuntary churn, the customer leaves the service due to relocation, death, etc. Businesses usually exclude involuntary churn from churn prediction models, and focus on voluntary churn, because it usually occurs due to company-customer relationship, on which the company has full control. Churn is usually measured as gross churn and net churn. Gross churn is calculated as loss of previous customers and their associated recurring revenue, generated by those customers. Net churn is measured as sum of Gross Churn and addition of new similar customers. This is often measure as Recurring Monthly Revenue (RMR) in the Financial Systems.

客户流失可以分为自愿流失和非自愿流失。在自愿流失中，客户决定转到另一个服务提供商，而在非自愿流失中，客户由于搬迁、死亡等原因离开服务。企业通常将非自愿流失排除在流失预测模型之外，而将重点放在自愿流失上，因为这通常是由于公司与客户的关系而发生的，而公司对这种关系拥有完全的控制权。用户流动率通常以总用户流动率和净用户流动率来衡量。总流失率是根据以前客户的损失以及这些客户产生的相关经常性收入来计算的。净流失率是指总流失率和新增类似客户的总和。在财务系统中，这通常被衡量为每月经常性收入(RMR)。

1.INTRODUCTION 引言

Predicting and preventing customer churn is becoming the primary focus of many enterprises. Every enterprise wants to retain its each and every customer, in order to maximize maximum profits and revenue from them. With the introduction of business and management systems, and automation of operation flow, corporates have gathered lots of customer and business related data during the daily operating activities, which give data mining techniques a good ground for working and predicting. Lots of data mining algorithms and models have emerged to rescue from this issue of customer loss. These algorithms have been widely used, from past decades, in this field.

预测和防止客户流失成为许多企业的首要关注点。每个企业都想留住自己的每一个客户，以便从他们那里获得最大的利润和收入。随着业务和管理系统的引入，以及业务流程的自动化，企业在日常经营活动中收集了大量的客户和业务相关数据，这为数据挖掘技术的工作和预测提供了良好的基础。为了解决这一客户流失问题，出现了大量的数据挖掘算法和模型。在过去的几十年里，这些算法在这一领域得到了广泛的应用。

For prediction of customer churn, many algorithms and models have been applied. Most common of them are Decision tree [1], Artificial Neural Network [2], Logistic Regression [8]. In addition, other algorithms such as Bayesian Network [4], Support Vector Machine [], Rough set [5], and Survival Analysis [6] have also been used.

In addition of algorithms and models, other techniques, such as input variable selection, feature selection, outlier detection, etc. have also been applied to get better results out of the above algorithms.

First three models i.e. Decision tree, Artificial Neural Network and Logistic Regression have been applied maturely at multiple corporates. Each algorithm has been improved over multiple iterations, and are now pretty much stable. But as the operation and activities of business are growing, it is becoming more and more complex challenge to solve the problem of customer churn, and this is requesting for the generation of new churn prediction models, which are fast and robust, and which can quickly be trained and scored on large amounts of data.

2.Literature review 文献综述

Jiayin and Yuanquan [1] presented a step by step approach on selecting effective input variables for customer churn prediction model in telecommunication industry. In telecommunication industry, there are usually very large number of input variables is available for churn prediction models. Of all these variables, there could be variables which have positive effect on the model, and few which are redundant. These redundant variables cause overload for the churn prediction model. So it is always better to select only important features and remove redundant, noisy and less informative variables. In their study, they have proposed Area under ROC (AUC) method for calculating classifying abilities of the variable, where ROC is Receiver Operating Characteristics, and then selecting variables which have the highest classifying abilities. In addition, he also proposed to compute mutual information among all selected variables and finally selecting variables which have relatively low mutual information co-efficient.

Jiayin和Yuanquan[1]提出了电信行业客户流失预测模型中有效输入变量选择的分步方法。在电信行业，通常有大量的输入变量可用于用户流失预测模型。在所有这些变量中，可能存在对模型有积极影响的变量，而冗余的变量很少。这些冗余变量会导致人员流失率预测模型过载。因此，最好只选择重要的特征，去除冗余的、有噪声的和信息量较小的变量。在他们的研究中，他们提出了Area under ROC (AUC)方法来计算变量的分类能力，其中ROC为Receiver Operating Characteristics，然后选择具有最高分类能力的变量。此外，他还提出了计算所有被选择变量之间的互信息，最终选择互信息系数相对较低的变量。

Huang and Kechadi [11] proposed a new technique for Feature Selection for the churn prediction models. As their primary focus was telecommunication industry, and in telecom the amount of input variables / feature is very large, and it is always better to select a subset of features, which have the most ability to classify the target classes. Otherwise running algorithm on all the input variables will be too much to time and resource consuming. Most commonly used techniques for selection of features only judges whether an input feature is helpful to classify the classes or not. The approach proposed by them takes into account the relationship between the specified categorical value of the feature and a class for selecting or removing the feature.

Luo, Shoa and Lie [2] proposed the customer churn prediction using Decision Tree for Personal Handyphone System Service (PHSS), where the number of variables in input data set is very small. Decision Tree is probably the most commonly used data mining algorithm. Decision Tree model is a predictive model that predicts using a classification process. It is represented as upside down Tree, in which root is at the top and leaves are at the bottom. Decision Trees is the representation of rules. This helps us in understanding, why a record has been classified in a particular way. And these rules can be used to find records that fall into some specific category. In their work they found out the optimal values of input dataset with reference to time sub-period, cost of misclassification and sampling method. With their research, they came up to conclusion that 10-days of sub-period, 1:5 cost of misclassification and random sampling method are the most optimal parameters when training a data model using decision trees, when the number of input variables is very small.

Ming, Huili and Yuwei [4] proposed a model for churn prediction using Bayesian Network. The concept of Bayesian Network was initially proposed by Judea Pearl (1986). This is a kind of graphics mode used to show the joint probability among different variables. It provides a natural way to describe the causality information which could be used in discovering the potential relations in data. This algorithm has been successively used in knowledge representation of expert system, data mining and machine learning. Recently, it has also been applied in fields of artificial intelligence, including causal reasoning, uncertain knowledge representation, pattern recognition cluster analysis and etc.

A Bayesian network consists of many nodes representing attributes connected by some lines, so the problems are concerned that more than one attribute determine another one which involving the theory of multiple probability distribution. Besides, since different Bayesian networks have different structures and some conceptions in graph theory such as tree, graph and directed acyclic graph can describe these structures clearly, graph theory is an important theoretical foundation of Bayesian networks as well as the probability theory, thus the results of Customer Churn using Bayesian network are very promising.

贝叶斯网络是由多条线连接的多个节点组成的，因此多属性决定多属性的问题涉及到多重概率分布理论。此外，由于不同的贝叶斯网络具有不同的结构，而图论中的一些概念如树、图、有向无环图等能够清楚地描述这些结构，图论是贝叶斯网络和概率论的重要理论基础，因此，利用贝叶斯网络进行客户流失分析的结果是很有前景的。

Jiayin, Yangming, Yingying and Shuang [10] proposed a new algorithm for churn prediction and called it TreeLogit. This algorithm is combination of ADTree and Logistic Regression models. It incorporates the advantages of both algorithms and making it equally good as TreeNet® Model which won the best prize in 2003 customer churn prediction contest. As Treelogit combines the advantages of both base algorithms so it becomes very powerful tool for customer churn prediction.

The Modeling process of TreeLogit starts by Designing Customer’s character variables based on prior knowledge. Then the character variables are categorized into m sub-vectors, and a decision tree for each sub-vector is created. Once we have the decision tree for each sub-vector, then we develop logistic regression models for each sub-vector. And finally we evaluate the accuracy and interpretability of the model. If they are acceptable then the customer retention process is started, otherwise the model is re-tuned for better results.

Jing and Xinghua [5] in their work on customer churn prediction, presented a model based on Support Vector Machines. Support Vector Machines are developed on the basis of statistical learning theory which is regarded as the best theory for the small sample estimation and predictive learning. The studies on the machine learning of finite sample were started by Vapnik in sixties of last century and a relatively complete theoretical system called statistical learning theory was set up in nineties. After that, Support Vector Machines, a new learning machine was proposed. SVM is built on the structural risk minimization principle that is to minimize the real error probability and is mainly used to solve the pattern recognition problems. Because of SVM’s complete theoretical framework and the good effects in practical application, it has been widely valued in machine learning field.

3.Rough set 粗糙集

Xu E, Liangeshan Shao, XXuedong Gao and Zhai Baofeng introduced Rough set algorithm for customer churn prediction [2]. Dengh Hu also studied the applications of rough set for customer churn prediction[5]. According to them, Rough set is a data analysis theory proposed by Z. Pawlak. Its main idea is to export the decision or classification rules by knowledge reduction at the premise of keeping the classification ability unchanged.

Xu E, Liangeshan Shao, xxudong Gao, Zhai Baofeng介绍了一种基于粗糙集的客户流失预测算法[2]。Denhu还研究了粗糙集在客户流失预测中的应用[5]。根据他们的观点，粗糙集是由Z. Pawlak提出的一种数据分析理论。其主要思想是在保持分类能力不变的前提下，通过知识约简输出决策规则或分类规则。

This theory has some unique views such as knowledge granularity which make Rough set theory especially suitable for data analysis. Rough set is built on the basis of classification mechanism and the space’s partition made by equivalence relation is regarded as knowledge. Generally speaking, it describes the imprecise or uncertain knowledge using the knowledge that has been proved. In this theory, knowledge is regarded as a kind of classification ability on data and the objects in the universe are usually described by decision table that is a two-dimensional table whose row represents an object and column an attribute. The attribute consists of decision attribute and condition attribute. The objects in the universe can be distributed into decision classes with different decision attributes according to the condition attributes of them. One of the core contents in the rough set theory is reduction that is a process in which some unimportant or irrelevant knowledge are deleted at the premise of keeping the classification ability unchanged. A decision table may have several reductions whose intersection was defined as the core of the decision table. The attribute of the core is important due to the effect to classification.

4.Survival Analysis 生存分析

Survival analysis is a kind of Statistical Analysis method to analyze and deduce the life expectancy of the creatures or products according to the data comes from surveys or experiments. It always combines the consequences of some events and the corresponding time span to analyze some problems. It was initially used in medical science to study the medicines’ influence to the life expectancy of the research objects.

生存分析是一种统计分析方法，根据调查或实验得到的数据来分析和推断生物或产品的预期寿命。它总是结合一些事件的后果和相应的时间跨度来分析一些问题。它最初用于医学研究药物对研究对象寿命的影响。

The survival time should be acknowledged widely, that is, the duration of some condition in nature, society or technical process. In this paper, the churn of a customer is regarded as the end of the customer’s survival time. In the fifties of last century, the statisticians began to study the reliability of industrial products, which advanced the development of the survival analysis in theory and application. The proportional hazard regression model is a commonly used survival analysis technique which was first proposed by Cox in 1972.

5.CRITICAL REVIEW 评论

Jiayin and Yuanquan [1] proposed a very simple method for the variable selection. The method proposed is very effective and practical, But there are more systematic methods available, which use advance neural network, induction algorithms and rough set.

Jiayin和Yuanquan[1]提出了一种非常简单的变量选择方法。提出的方法是非常有效和实用的，但有更多系统的方法可用，使用先进的神经网络，归纳算法和粗糙集。

Huang’s and Kechadi’s [11] concept for taking into account the categorical values into account when feature selection is being performed, is good. But their concept is limited to categorical values and continues values can’t be applied on their approach. Continues values need to be discretized into categorical values, before their feature selection concept could be applied, but this conversion from continues to discrete may result in loss of information.

Luo, Shoa and Lie [2] selected Decision Tree as their choice of data mining algorithm for churn prediction, which is the simplest and understandable algorithm for classification. Its simplicity also makes it the most widely used algorithm. But decision tree has its own limitations, they are very unstable and a very little change in the input variables, such as addition of newer ones, require rebuilding and re-training of complete decision tree. In addition, they should have also focused on how to enrich the input variables, by adding new derived variables that could enhance the efficiency of the model.

Ming, Huili and Yuwei [4] Bayesian network model has advantages and some short comings. It has the ability to product best results even when the input datasets are incomplete. In addition, it has the ability to take connections into account when predicting churn and to take prior knowledge into consideration. This algorithm also has the ability to effectively prevent over fitting. But if the dataset is large, the structure learning of the Bayesian networks will be too difficult. Thus this model is not fit for telecom, where the dataset is always very large.

Jiayin, Yangming, Yingying and Shuang [10] TreeLogit combines the advantages of both algorithms i.e. ADTree and logistic regression, thus it is both data-driven and assumption-driven and it has the capability of analyzing objects with incomplete information. Moreover, its efficiency is not affected by the bad quality data and it generates continues output with relatively low complexity.

Jing and Xinghua [5] used Support Vector Machine algorithm for Churn Prediction. This algorithm is best if you have a limited number of sample records, but on the other hand its theory is very complex and there are many variations in it. So it is difficult to find the version which best suites your problem.

There are multiple solutions available for customer churn prediction. Each has its own advantages and disadvantages. So a single solution might not be best for any organization. The organization may have to use the combination of algorithms and techniques to get the best results for churn prediction.

有多种解决方案可以预测客户流失。每一种都有自己的优点和缺点。因此，单一的解决方案可能并不适合任何组织。组织可能必须结合使用算法和技术来获得最佳的人员流失预测结果。

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